1. Field
The present disclosure generally relates to superconducting computing, for example analog or quantum computing employing processors that operate at superconducting temperatures.
2. Description of the Related Art
A Turing machine is a theoretical computing system, described in 1936 by Alan Turing. A Turing machine that can efficiently simulate any other Turing machine is called a Universal Turing Machine (UTM). The Church-Turing thesis states that any practical computing model has either the equivalent or a subset of the capabilities of a UTM.
A quantum computer is any physical system that harnesses one or more quantum effects to perform a computation. A quantum computer that can efficiently simulate any other quantum computer is called a Universal Quantum Computer (UQC).
In 1981 Richard P. Feynman proposed that quantum computers could be used to solve certain computational problems more efficiently than a UTM and therefore invalidate the Church-Turing thesis. See e.g., Feynman R. P., “Simulating Physics with Computers”, International Journal of Theoretical Physics, Vol. 21 (1982) pp. 467-488. For example, Feynman noted that a quantum computer could be used to simulate certain other quantum systems, allowing exponentially faster calculation of certain properties of the simulated quantum system than is possible using a UTM.
Approaches to Quantum Computation
There are several general approaches to the design and operation of quantum computers. One such approach is the “circuit model” of quantum computation. In this approach, qubits are acted upon by sequences of logical gates that are the compiled representation of an algorithm. Circuit model quantum computers have several serious barriers to practical implementation. In the circuit model, it is required that qubits remain coherent over time periods much longer than the single-gate time. This requirement arises because circuit model quantum computers require operations that are collectively called quantum error correction in order to operate. Quantum error correction cannot be performed without the circuit model quantum computer's qubits being capable of maintaining quantum coherence over time periods on the order of 1,000 times the single-gate time. Much research has been focused on developing qubits with coherence sufficient to form the basic information units of circuit model quantum computers. See e.g., Shor, P. W. “Introduction to Quantum Algorithms”, arXiv.org:quant-ph/0005003 (2001), pp. 1-27. The art is still hampered by an inability to increase the coherence of qubits to acceptable levels for designing and operating practical circuit model quantum computers.
Another approach to quantum computation, involves using the natural physical evolution of a system of coupled quantum systems as a computational system. This approach does not make critical use of quantum gates and circuits. Instead, starting from a known initial Hamiltonian, it relies upon the guided physical evolution of a system of coupled quantum systems wherein the problem to be solved has been encoded in the terms of the system's Hamiltonian, so that the final state of the system of coupled quantum systems contains information relating to the answer to the problem to be solved. This approach does not require long qubit coherence times. Examples of this type of approach include adiabatic quantum computation, cluster-state quantum computation, one-way quantum computation, quantum annealing and classical annealing, and are described, for example, in Farhi, E. et al., “Quantum Adiabatic Evolution Algorithms versus Simulated Annealing” arXiv.org:quant-ph/0201031 (2002), pp 1-24.
Qubits
As mentioned previously, qubits can be used as fundamental units of information for a quantum computer. As with bits in UTMs, qubits can refer to at least two distinct quantities; a qubit can refer to the actual physical device in which information is stored, and it can also refer to the unit of information itself, abstracted away from its physical device.
Qubits generalize the concept of a classical digital bit. A classical information storage device can encode two discrete states, typically labeled “0” and “1”. Physically these two discrete states are represented by two different and distinguishable physical states of the classical information storage device, such as direction or magnitude of magnetic field, current, or voltage, where the quantity encoding the bit state behaves according to the laws of classical physics. A qubit also contains two discrete physical states, which can also be labeled “0” and “1”. Physically these two discrete states are represented by two different and distinguishable physical states of the quantum information storage device, such as direction or magnitude of magnetic field, current, or voltage, where the quantity encoding the bit state behaves according to the laws of quantum physics. If the physical quantity that stores these states behaves quantum mechanically, the device can additionally be placed in a superposition of 0 and 1. That is, the qubit can exist in both a “0” and “1” state at the same time, and so can perform a computation on both states simultaneously. In general, N qubits can be in a superposition of 2N states. Quantum algorithms make use of the superposition property to speed up some computations.
In standard notation, the basis states of a qubit are referred to as the |0 and |1 states. During quantum computation, the state of a qubit, in general, is a superposition of basis states so that the qubit has a nonzero probability of occupying the |0 basis state and a simultaneous nonzero probability of occupying the |1 basis state. Mathematically, a superposition of basis states means that the overall state of the qubit, which is denoted |Ψ, has the form |Ψ=a |0+b|1, where a and b are coefficients corresponding to the probabilities |a|2 and |b|2, respectively. The coefficients a and b each have real and imaginary components, which allows the phase of the qubit to be characterized. The quantum nature of a qubit is largely derived from its ability to exist in a coherent superposition of basis states and for the state of the qubit to have a phase. A qubit will retain this ability to exist as a coherent superposition of basis states when the qubit is sufficiently isolated from sources of decoherence.
To complete a computation using a qubit, the state of the qubit is measured (i.e., read out). Typically, when a measurement of the qubit is performed, the quantum nature of the qubit is temporarily lost and the superposition of basis states collapses to either the |0 basis state or the |1 basis state and thus regaining its similarity to a conventional bit. The actual state of the qubit after it has collapsed depends on the probabilities |a|2 and |b|2 immediately prior to the readout operation.
Superconducting Qubits
There are many different hardware and software approaches under consideration for use in quantum computers. One hardware approach uses integrated circuits formed of superconducting materials, such as aluminum or niobium. The technologies and processes involved in designing and fabricating superconducting integrated circuits are similar to those used for conventional integrated circuits.
Superconducting qubits are a type of superconducting device that can be included in a superconducting integrated circuit. Superconducting qubits can be separated into several categories depending on the physical property used to encode information. For example, they may be separated into charge, flux and phase devices, as discussed in, for example Makhlin et al., 2001, Reviews of Modern Physics 73, pp. 357-400. Charge devices store and manipulate information in the charge states of the device, where elementary charges consist of pairs of electrons called Cooper pairs. A Cooper pair has a charge of 2 e and consists of two electrons bound together by, for example, a phonon interaction. See e.g., Nielsen and Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000), pp. 343-345. Flux devices store information in a variable related to the magnetic flux through some part of the device. Phase devices store information in a variable related to the difference in superconducting phase between two regions of the phase device. Recently, hybrid devices using two or more of charge, flux and phase degrees of freedom have been developed. For practical superconducting quantum computing systems, superconducting qubits are coupled together. See e.g., U.S. Pat. No. 6,838,694 and U.S. Patent Application No. 2005-0082519.
Persistent Current Coupler
In FIG. 1A shows schematic diagram of a controllable coupler 100. This coupler is a loop of superconducting material 101 interrupted by a single Josephson junction 102 and is used to couple a first qubit 110 and a second qubit 120 for use in an analog computer. The first qubit 110 is comprised of a loop of superconducting material 111 interrupted by a compound Josephson junction 112 and is coupled to the controllable coupler 100 through the exchange of flux 103 between the coupler 100 and the first qubit 110. The second qubit 120 is comprised of a loop of superconducting material 121 interrupted by a compound Josephson junction 122 and is coupled to the controllable coupler 100 through the exchange of flux 104 between the coupler 100 and the second qubit 120. Flux 105 created by electrical current flowing through a magnetic flux transformer 130 is applied to the loop of superconducting material 101.
Flux 105 produced by the magnetic flux transformer 130 is applied to the loop of superconducting material 101 and controls the state of the controllable coupler 100. The controllable coupler 100 is capable of producing a zero coupling between the first qubit 110 and the second qubit 120, an anti-ferromagnetic coupling between the first qubit 110 and the second qubit 120, and a ferromagnetic coupling between the first qubit 110 and the second qubit 120.
FIG. 1B shows an exemplary two-pi-periodic graph 150B giving the relationship between the persistent current (I) flowing within the loop of superconducting material 101 of the controllable coupler 100 (Y-axis) as a function of the flux (Φx) 105 from the magnetic flux transformer 130 applied to the loop of superconducting material 101 and scaled with the superconducting flux quantum Φ0 (X-axis).
Zero coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to point 160B or any other point along the graph 150B with a similar slope of about zero of point 160B. Anti-ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 170B or any other point along the graph 150 with a similar positive slope of point 170B. Ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 180B or any other point along the graph 150 with a similar negative slope of point 180B.
The coupler is set to states 160B, 170B and 180B by adjusting the amount of flux 105 coupled between the magnetic flux transformer 130 and the loop of superconducting material 101. The state of the coupler is dependant upon the slope of the graph 150B. For dI/dΦx equal to zero, the coupler is said to produce a zero coupling or non-coupling state where the quantum state of the first qubit 110 does not interact with the state of the second qubit 120. For dI/dΦx greater than zero, the coupler is said to produce an anti-ferromagnetic coupling where the state of the first qubit 110 and the state of the second qubit 120 will be dissimilar in their lowest energy state. For dI/dΦx less than zero, the coupler is said to produce a ferromagnetic coupling where the state of the first qubit 110 and the state of the second qubit 120 will be similar in their lowest energy state. Those of skill in the art would appreciate that depending upon the configuration of the coupler; anti-ferromagnetic coupling may be associated with dI/dΦx less than zero whereas ferromagnetic coupling may be associated with dI/dΦx greater than zero. From the zero coupling state with corresponding flux level 161, the amount of flux (Φx) 105 produced by the magnetic flux transformer 130 applied to the loop of superconducting material 101 can be decreased to a flux level 171 to produce an anti-ferromagnetic coupling between the first qubit 110 and the second qubit 120 or increased to a flux level 181 to produce a ferromagnetic coupling between the first qubit 110 and the second qubit 120.
Examining the persistent current 162 that exists at the zero coupling point 160B, with corresponding zero coupling applied flux 161, shows a large persistent current is coupled into the first qubit 110 and the second qubit 120. This is not ideal as there may be unintended interactions between this persistent current flowing through the controllable coupler 100 and other components within the analog processor in which the controllable coupler 100 exists. Both anti-ferromagnetic coupling persistent current level 172 and ferromagnetic coupling persistent current level 182 may be of similar magnitudes as compared to zero coupling persistent current level 162 thereby causing similar unintended interactions between the persistent current of the coupler 100 and other components within the analog processor in which the controllable coupler 100 exists. Anti-ferromagnetic coupling persistent current level 172 and ferromagnetic coupling persistent current level 182 may be minimized such that the persistent current levels 172 and 182 are about zero during regular operations.
FIG. 1C shows a graph 150C giving the relationship between the coupling strength (of arbitrary units) between the first qubit 110 and the second qubit 120 (Y-axis) as a function of the flux bias 105 from the magnetic flux transformer 130 applied to the loop of superconducting material 101 and scaled by the superconducting flux quantum Φ0 (X-axis).
Zero coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to point 160C or any other point along the graph 150C with a similar coupling strength of zero as is exhibited by point 160C. Anti-ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 170C or any other point along the graph 150C with a coupling strength greater than zero as is exhibited by point 170C. Ferromagnetic coupling exists between the first qubit 110 and the second qubit 120 when the coupler 100 is set to the point 180B or any other point along the graph 150C with a coupling strength less than zero as is exhibited by point 180C.
The coupling response of the controllable coupler 100 to an applied flux bias 105 is very non-symmetric in nature in relation to anti-ferromagnetic and ferromagnetic responses. When anti-ferromagnetic coupling is created, adjustments to the amount of flux bias 105 applied to the loop of superconducting material 101 can be conducted over a large region of applied flux 105 while affecting the anti-ferromagnetic coupling very little. For example, applying a flux 105 of approximately −0.5Φ0 to 0.5Φ0 to the loop of superconducting material 101 results in anti-ferromagnetic coupling produced by the controllable coupler 100 between the first qubit 110 and the second qubit 120. When ferromagnetic coupling is created, adjustments to the amount of flux bias 105 applied to the loop of superconducting material 101 can be conducted over only a very small region of applied flux 105 while maintaining the ferromagnetic coupling state. For example, applying a flux 105 of approximately 0.95Φ0 to 1.05Φ0 to the loop of superconducting material 101 results in ferromagnetic coupling produced by the controllable coupler 100 between the first qubit 110 and the second qubit 120. Therefore it can be seen that while one form of coupling is attainable with limited precision with regards to control over the amount of flux bias 105 being applied to the loop of superconducting material 101, a coupling requires much greater precision. Also, zero coupling requires a very precise amount of flux bias 105 to be applied to the superconducting loop 101 to be achieved. Without very accurate control over the flux bias 105 being applied to the controllable coupler 100, the coupling produced by the controllable coupler 100 may not, in practice be what is desired.
For further discussion of the persistent current couplers, see e.g., Harris, R., “Sign and Magnitude Tunable Coupler for Superconducting Flux Qubits”, arXiv.org: cond-mat/0608253 (2006), pp. 1-5, and van der Brink, A. M. et al., “Mediated tunable coupling of flux qubits,” New Journal of Physics 7 (2005) 230.